Tatiana Petrova

Tatiana Petrova, Stanislav Sokol, Radu State

Which persuasion strategies, if any, are associated with donation compliance? Answering this requires fine-grained strategy labels across a full corpus and statistical tests corrected for multiple comparisons. We annotate all 10,600 persuader turns in the 1,017-dialogue PersuasionForGood corpus (Wang et al., 2019), where donation outcomes are directly observable, with a taxonomy of 41 strategies in 11 categories, using three open-source large language models (LLMs; Qwen3:30b, Mistral-Small-3.2, Phi-4). Strategy categories alone explain little variance in donation outcome (pseudo $R^2 \approx 0.015$, consistent across all three annotators). Guilt Induction is the only strategy significantly associated with lower donation rates ($Δ\approx -23$ percentage points), an effect that replicates across all three models despite only moderate inter-model agreement. Reciprocity is the most robust positive correlate. Target sentiment and interest predict whether a donation occurs but show at most a weak correlation with donation amount. These findings suggest that strategy identification alone is insufficient to explain persuasion effectiveness, and that guilt-based appeals may be counterproductive in prosocial settings. We release the fully annotated corpus as a public resource.

Tatiana Petrova, Evgeny Polyachenko, Radu State

We study the thermodynamic memory capacity of modern Hopfield networks (Dense Associative Memory models) with continuous states under geometric constraints, extending classical analyses of pairwise associative memory. We derive thermodynamic phase boundaries for Dense Associative Memory networks with exponential capacity $p = e^{αN}$, comparing Gaussian (LSE) and Epanechnikov (LSR) kernels. For continuous neurons on an $N$-sphere, the geometric entropy depends solely on the spherical geometry, not the kernel. In the sharp-kernel regime, the maximum theoretical capacity $α= 0.5$ is achieved at zero temperature; below this threshold, a critical line separates retrieval from a spin-glass phase. The two kernels differ qualitatively in their phase boundary structure: for LSE, the retrieval region extends to arbitrarily high temperatures as $α\to 0$, but interference from spurious patterns is always present. For LSR, the finite support introduces a threshold $α_{\text{th}}$ below which no spurious patterns contribute to the noise floor, producing a qualitatively different retrieval regime in this sub-threshold region. These results advance the theory of high-capacity associative memory and clarify fundamental limits of retrieval robustness in modern attention-like memory architectures.

Arkadii Kazanskii, Tatiana Petrova, Konstantin Bagrianskii et al.

Drifting Models [Deng et al., 2026] train a one-step generator by evolving samples under a kernel-based drift field, avoiding ODE integration at inference. The original analysis leaves two questions open. The drift-field iteration admits a locally repulsive regime in a two-particle surrogate, and vanishing of the drift ($V_{p,q}\equiv 0$) is not known to force the learned distribution $q$ to match the target $p$. We derive a contraction threshold for the surrogate and show that a linearly-scheduled friction coefficient gives a finite-horizon bound on the error trajectory. Under a Gaussian kernel we prove that the drift-field equilibrium is identifiable: vanishing of $V_{p,q}$ on any open set forces $q=p$, closing the converse of Proposition 3.1 of Deng et al. Our friction-augmented model, DMF (Drifting Model with Friction), matches or exceeds Optimal Flow Matching on FFHQ adult-to-child domain translation at 16x lower training compute.

Timur Mudarisov, Mikhal Burtsev, Tatiana Petrova et al.

We present a geometric framework for analysing multi-head attention in large language models (LLMs). Without altering the mechanism, we view standard attention through a top-N selection lens and study its behaviour directly in value-state space. We define geometric metrics - Precision, Recall, and F-score - to quantify separability between selected and non-selected tokens, and derive non-asymptotic bounds with explicit dependence on dimension and margin under empirically motivated assumptions (stable value norms with a compressed sink token, exponential similarity decay, and piecewise attention weight profiles). The theory predicts a small-N operating regime of strongest non-trivial separability and clarifies how sequence length and sink similarity shape the metrics. Empirically, across LLaMA-2-7B, Gemma-7B, and Mistral-7B, measurements closely track the theoretical envelopes: top-N selection sharpens separability, sink similarity correlates with Recall. We also found that in LLaMA-2-7B heads specialize into three regimes - Retriever, Mixer, Reset - with distinct geometric signatures. Overall, attention behaves as a structured geometric classifier with measurable criteria for token selection, offering head level interpretability and informing geometry-aware sparsification and design of attention in LLMs.

Tatiana Petrova

Understanding whether retrieval in dense associative memories survives thermal noise is essential for bridging zero-temperature capacity proofs with the finite-temperature conditions of practical inference and biological computation. We use Monte Carlo simulations to map the retrieval phase boundary of two continuous dense associative memories (DAMs) on the $N$-sphere with an exponential number of stored patterns $M = e^{αN}$: a log-sum-exp (LSE) kernel and a log-sum-ReLU (LSR) kernel. Both kernels share the zero-temperature critical load $α_c(0)=0.5$, but their finite-temperature behavior differs markedly. The LSE kernel sustains retrieval at arbitrarily high temperatures for sufficiently low load, whereas the LSR kernel exhibits a finite support threshold below which retrieval is perfect at any temperature; for typical sharpness values this threshold approaches $α_c$, making retrieval nearly perfect across the entire load range. We also compare the measured equilibrium alignment with analytical Boltzmann predictions within the retrieval basin.

Tatiana Petrova, Boris Bliznioukov, Aleksandr Puzikov et al.

The concept of the Web of Agents (WoA), which transforms the static, document-centric Web into an environment of autonomous agents acting on users' behalf, has attracted growing interest as large language models (LLMs) become more capable. However, research in this area is still fragmented across different communities. Contemporary surveys catalog the latest LLM-powered frameworks, while the rich histories of Multi-Agent Systems (MAS) and the Semantic Web are often treated as separate, legacy domains. This fragmentation obscures the intellectual lineage of modern systems and hinders a holistic understanding of the field's trajectory. We present the first comprehensive evolutionary overview of the WoA. We show that modern protocols like A2A and the MCP, are direct evolutionary responses to the well-documented limitations of earlier standards like FIPA standards and OWL-based semantic agents. To systematize this analysis, we introduce a four-axis taxonomy (semantic foundation, communication paradigm, locus of intelligence, discovery mechanism). This framework provides a unified analytical lens for comparing agent architectures across all generations, revealing a clear line of descent where others have seen a disconnect. Our analysis identifies a paradigm shift in the 'locus of intelligence': from being encoded in external data (Semantic Web) or the platform (MAS) to being embedded within the agent's core model (LLM). This shift is foundational to modern Agentic AI, enabling the scalable and adaptive systems the WoA has long envisioned. We conclude that while new protocols are essential, they are insufficient for building a robust, open, trustworthy ecosystem. Finally, we argue that the next research frontier lies in solving persistent socio-technical challenges, and we map out a new agenda focused on decentralized identity, economic models, security, and governance for the emerging WoA.

Timur Mudarisov, Mikhail Burtsev, Tatiana Petrova et al.

This paper investigates the limitations of the normalization in attention mechanisms. We begin with a theoretical framework that enables the identification of the model's selective ability and the geometric separation involved in token selection. Our analysis includes explicit bounds on distances and separation criteria for token vectors under softmax scaling. Through experiments with pre-trained GPT-2 model, we empirically validate our theoretical results and analyze key behaviors of the attention mechanism. Notably, we demonstrate that as the number of selected tokens increases, the model's ability to distinguish informative tokens declines, often converging toward a uniform selection pattern. We also show that gradient sensitivity under softmax normalization presents challenges during training, especially at low temperature settings. These findings advance current understanding of softmax-based attention mechanism and motivate the need for more robust normalization and selection strategies in future attention architectures.